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Properties

Label 6.9
Level 6
Weight 9
Dimension 2
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 18
Trace bound 0

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Defining parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(6))\).

Total New Old
Modular forms 10 2 8
Cusp forms 6 2 4
Eisenstein series 4 0 4

Trace form

\( 2 q - 126 q^{3} - 256 q^{4} - 1152 q^{6} + 5572 q^{7} + 2754 q^{9} - 13056 q^{10} + 16128 q^{12} - 26300 q^{13} - 58752 q^{15} + 32768 q^{16} + 145152 q^{18} + 288004 q^{19} - 351036 q^{21} - 507648 q^{22}+ \cdots + 287836416 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(6))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
6.9.b \(\chi_{6}(5, \cdot)\) 6.9.b.a 2 1

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(6))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(6)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)